Recovery of dipolar sources and stability estimates

Abstract

The inverse problem of identifying dipolar sources with time-dependent moments, located in a bounded domain, via the heat equation is investigated, by applying a heat flux, and from a single lateral boundary measurement of temperature. An uniqueness, and local Lipschitz stability results for this inverse problem are established which are the main contributions of this work. A non-iterative algebraic algorithm based on the reciprocity gap concept is proposed, which permits to determine the number, the spatial locations, and the time-dependent moments of the dipolar sources, Some numerical experiments are given in order to test the efficiency and the robustness of this method.

The inverse problem of dipolar source identification from incomplete boundary measurements

“…Recently, it has been used for modelling of plasma confinement in a tokamak reactor [48]. On the other hand, many works have investigated the point sources identification problem using the reciprocity gap (RG) principle for elliptic equations; see, for example, [36,[49][50][51][52][53][54][55]. The authors showed that the appropriate selection of harmonic fields leads to the identification of positions and intensities.…”

“…For stability, many works have been interested in this question. A local Lipschitz stability results derived from algebraic relations for elliptic sources identification problems [49], for dipolar sources with time‐dependent moments using Gateaux differentiability [54], and for a linear combination of monopolar and dipolar sources, with an estimation of the Lipschitz constant, when the measured data are available on the whole boundary [55].…”